Kellogg Synthesis Reactor Properties
Density of ammonia = 0.73 kg/m³
Tube diameter = 0.084 m
Tube cross-sectional area = 0.005542488 m²
Total number of tubes = 460
Length of tube = 20 ft
Iron filling diameter, dp = 0.0050 m
= 5 mm
Assume:
Diffusivity, Dab = 1.88E-05 m²/s
Rate constant, kr = 0.00016
Reactor volume, V = 61.0726 m³
Diameter of reactor = 3.6 m
Specific heat capacity, Cp = 7.31 kJ/kg·K
Prandtl number, Pr = 1.410088609686E-06
heat conductivity, k = 79.5
Let:
Mass flow rate = 12000 kg/h
Hence,
Total volumetric flow rate = 4.5662100456621 m³/s
Volumetric flow rate/tube = 0.009926543577526 m³/s
Velocity of flow = 1.79099054026392 m/s
Dynamic viscosity = 1.5335437E-05 kg/m·s
= 0.00015335437 Poise
Kinematic vicosity = 2.100744794521E-05 m²/s
Reynold number determination:
Reynold number, NRE = ρDv/μ
= 7161.42226197947 ( >4000, turbulent flow)
Frossling Marshall equation:
Sh=2+0.6Re^(1/2)*Sc^(1/3)
Sh=Kgdp/Dab
Sc=v/Dab
Hence,
Schmidt number, Sc = 1.12
Sherwood number, Sh = 54.69
For most fluid:
Sh = 0.6Re^(1/2)*Sc^(1/3)
kg*dp/Dab = 0.6Re^(1/2)*Sc^(1/3)
Mass transfer coefficient, kg = 0.1981 m/s
At steady state,
ras = kg(Cab-Cas)
ras = Ks(PN2- PNH32/Ke)
Hence,
kg(Cab-Cas) = Ks(PN2- PNH32/Ke)
N2 is the gas involved in rate limiting step.
Cab = concentration of N2 gas
PN2 = 8 atm
R = 0.08206 L·atm/(K·mol)
T = 673 K
From ideal gas law: PN2= CN2RT
CN2 = PN2/RT
= 0.144858308656117 mol/L
jD = kg*ᵽ/G*Sc^1/3
= 3.010E-04
assume jD=jH
h = 58.3192
From the graph, we found that
Cab = 0.14486
Cas = 0.13679
Amount of heat released = 13496750.261183 J
13496.750261183 kJ/s
3 criteria to be met:
Cwp < 1
………….. < 0.15
………….. < 0.15
heat conductivitiy, k = 79.5 W/m^2*K
Nusselt number=
2.25644114650553 h = Nu * k/L
49.82974199
Calculated parameters:
Diffusivity, Dab = 1.88E-05 m²/s
Kinematic vicosity = 2.10E-05 m²/s
Iron filling diameter, dp = 0.005 m
Rate constant, k = 1.60E-04 0.001
External Mass Transfer:
Volumetric Fluid Mass Transfer Cao-Cas, Reaction
flow rate(m³/s) velocity (m²/s) Cao rate coefficient, kg Cas ΔC rate, -rA U/dp (U/dp)^1/2
0.007031 0.0027792 0.14486 0.0042577 0.121947 0.0229131 2.2338E-05 2.779171 1.667085
0.017578 0.0069479 0.14486 0.0067321 0.074261 0.0705986 2.2640E-05 6.947927 2.635892
0.043946 0.0173698 0.14486 0.0106443 0.090466 0.0543938 2.2834E-05 17.369817 4.167711
0.109864 0.0434245 0.14486 0.0168301 0.104950 0.0399095 2.2959E-05 43.424543 6.589730
0.274660 0.1085614 0.14486 0.0266108 0.116775 0.0280849 2.3039E-05 108.561357 10.419278
0.686651 0.2714034 0.14486 0.0420753 0.125735 0.0191253 2.3090E-05 271.403394 16.474325
1.716626 0.6785085 0.14486 0.0665269 0.132147 0.0127128 2.3122E-05 678.508484 26.048195
4.566210 1.8048261 0.14486 0.1085020 0.136791 0.0080687 2.3143E-05 1804.826105 42.483245
11.415525 4.5120653 0.14486 0.1715567 0.139650 0.0052097 2.3156E-05 4512.065263 67.171908
28.538813 11.2801632 0.14486 0.2712549 0.141521 0.0033391 2.3164E-05 11280.163157 106.208112
71.347032 28.2004079 0.14486 0.4288917 0.142730 0.0021298 2.3169E-05 28200.407893 167.929771
178.367580 70.5010197 0.14486 0.6781373 0.143506 0.0013544 2.3172E-05 70501.019732 265.520281
Graph of ΔC vs Fluid Velocity
0.080
0.070
0.060
Cao-Cas, ΔC
0.050
0.040
0.030
0.020
0.010
0.000
0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0
Fluid velocity (m/s)
R eaction rate, -rA
2.34E-05
Graph of -rA vs (U/dp)^1/2
2.32E-05
2.30E-05
2.28E-05
2.26E-05
2.24E-05
2.22E-05
2.20E-05
2.18E-05
0 50 100 150 200 250 300
(U/dp)^1/2
2.24E-05
2.22E-05
2.20E-05
2.18E-05
0 50 100 150 200 250 300
(U/dp)^1/2
Diffusivity, Dab = 1.88E-05 m²/s
0.4
0.8
3
2.005333E-06
R radius of catalyst 0.0025
ras = 0.001599
Density of ammonia = 0.73 kg/m³
Cas = 0.13679
0.1630696056
6.18663
0.9985802383 approximately equal to 1
Cab = 0.14486
1.0589955406
1.1198793327
0.06733
k_c 0.2
0.008482
ately equal to 1
